The Minimum Volume Covering Ellipsoid Estimation in Kernel-Defined Feature Spaces

Dolia, Alexander N.; Bie, Tijl De; Harris, C.J.; Shawe‐Taylor, John; Titterington, D. M.

doi:10.1007/11871842_61

Cited by 17 publications

(8 citation statements)

References 6 publications

(12 reference statements)

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“…28 The first approach based on deep learning is the deep-SVDD. 29 Alternatively, there are other approaches that employ a set of ellipsoids to fit the region of the data space, 30,31 or others that employ a family of convex hulls for one-class classification 32 like the well-known approximate polytope ensemble algorithm (APE). 33 Within the boundary approach, there can also be found ensembles-based methods like the one-class random forests (OCRF).…”

Section: Related Workmentioning

confidence: 99%

DSVD‐autoencoder: A scalable distributed privacy‐preserving method for one‐class classification

2020

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One-class classification has gained interest as a solution to certain kinds of problems typical in a wide variety of real environments like anomaly or novelty detection. Autoencoder is the type of neural network that has been widely applied in these one-class problems. In the Big Data era, new challenges have arisen, mainly related with the data volume. Another main concern derives from Privacy issues when data is distributed and cannot be shared among locations. These two conditions make many of the classic and brilliant methods not applicable. In this paper, we present distributed singular value decomposition (DSVDautoencoder), a method for autoencoders that allows learning in distributed scenarios without sharing raw data. Additionally, to guarantee privacy, it is noniterative and hyperparameter-free, two interesting characteristics when dealing with Big Data. In comparison with the state of the art, results demonstrate that DSVD-autoencoder provides a highly competitive solution to deal with very large data sets by reducing training from several hours to seconds while maintaining good accuracy.

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Section: Related Workmentioning

confidence: 99%

DSVD‐autoencoder: A scalable distributed privacy‐preserving method for one‐class classification

2020

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“…where Φ is the vector of dual variables φ j , γ ≥ 0 and γI is an extra constraint that guarantees a minimal diameter of the ellipsoid in all directions. This would prevent the ellipsoid from collapsing to zero volume especially in large dimensional spaces [6].…”

Section: Fast Computation Of the Mvce: Letmentioning

confidence: 99%

Local Metric Learning on Manifolds with Application to Query–Based Operations

Abou–Moustafa

Ferrie

2008

Lecture Notes in Computer Science

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We first investigate the combined effect of data complexity, curse of dimensionality and the definition of the Euclidean distance on the distance measure between points. Then, based on the concepts underlying manifold learning algorithms and the minimum volume ellipsoid metric, we design an algorithm that learns a local metric on the lower dimensional manifold on which the data is lying. Experiments in the context of classification on standard benchmark data sets showed very promising results when compared to state of the art algorithms, and consistent improvements over the Euclidean distance in the context of query-based learning.

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“…To address both issues we propose a generalization of the MRCD which is defined in a kernel-induced feature space F, where the proposed estimator exploits the kernel trick: the p × p covariance matrix is not calculated explicitly but replaced by the calculation of a n × n centered kernel matrix, resulting in a computational speed-up in case n p. Similar ideas can be found in the literature, see e.g. Dolia et al (2006Dolia et al ( , 2007 which kernelized the minimum volume ellipsoid (Rousseeuw 1984(Rousseeuw , 1985. The results of the KMRCD algorithm with the linear kernel k(x, y) = x y and radial basis function (RBF) kernel k(x, y) = e − x−y 2 /(2σ 2 ) are shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Outlier detection in non-elliptical data by kernel MRCD

et al. 2021

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The minimum regularized covariance determinant method (MRCD) is a robust estimator for multivariate location and scatter, which detects outliers by fitting a robust covariance matrix to the data. Its regularization ensures that the covariance matrix is well-conditioned in any dimension. The MRCD assumes that the non-outlying observations are roughly elliptically distributed, but many datasets are not of that form. Moreover, the computation time of MRCD increases substantially when the number of variables goes up, and nowadays datasets with many variables are common. The proposed kernel minimum regularized covariance determinant (KMRCD) estimator addresses both issues. It is not restricted to elliptical data because it implicitly computes the MRCD estimates in a kernel-induced feature space. A fast algorithm is constructed that starts from kernel-based initial estimates and exploits the kernel trick to speed up the subsequent computations. Based on the KMRCD estimates, a rule is proposed to flag outliers. The KMRCD algorithm performs well in simulations, and is illustrated on real-life data.

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The Minimum Volume Covering Ellipsoid Estimation in Kernel-Defined Feature Spaces

Cited by 17 publications

References 6 publications

DSVD‐autoencoder: A scalable distributed privacy‐preserving method for one‐class classification

DSVD‐autoencoder: A scalable distributed privacy‐preserving method for one‐class classification

Local Metric Learning on Manifolds with Application to Query–Based Operations

Outlier detection in non-elliptical data by kernel MRCD

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